The kind of conjunction that would complete both blanks in the sentence is a correlative conjunction, which connects two balanced clauses, phrases, or words. So, any of these correlative conjunctions would do: either/or, neither/nor, both/and, etc.
Correlative conjunctions are sort of like tag-team conjunctions. They come in pairs, and you have to use both of them in different places in a sentence to make them work. ... Correlative conjunctions include pairs such as "both/and," "either/or," "neither/nor," "not/but" and "not only/but also."
